name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.SubExpr.Pos.pushAppFn | Lean.SubExpr | [
"instOfNatNat",
"Lean.SubExpr.Pos",
"Lean.SubExpr.Pos.push",
"Nat",
"OfNat.ofNat"
] | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.exists_of_linearIndepOn_of_finite_span._simp_1_13 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Membership.mem",
"Iff",
"propext",
"Set.ext_iff",
"Eq",
"Set.instMembership",
"Set"
] | false |
MonoidAlgebra.liftNCAlgHom._proof_1 | Mathlib.Algebra.MonoidAlgebra.Basic | [
"AlgHom.algHomClass",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"CommSemiring",
"Semiring",
"AlgHomClass.toRingHomClass",
"Semiring.toNonAssocSemiring",
"RingHomClass"
] | false |
Std.Http.Chunk.mk.sizeOf_spec | Std.Internal.Http.Data.Chunk | [
"Std.Http.Chunk.mk",
"Std.Http.Chunk._sizeOf_inst",
"Option._sizeOf_inst",
"Std.Http.Chunk",
"ByteArray._sizeOf_inst",
"Std.Http.Chunk.ExtensionName._sizeOf_inst",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Std.Http.Chunk.ExtensionValue",
"SizeOf.sizeOf... | true |
ContDiffWithinAt.congr_of_mem | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedSpace",
"Membership.mem",
"ContDiffWithinAt.congr",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"ContDiffWithinAt",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"Set.instMembership",
"NormedAddCommGroup",
"WithTop",
"Set"
] | true |
isIntegral_algebraMap_iff | Mathlib.RingTheory.IntegralClosure.IsIntegral.Basic | [
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsScalarTower",
"IsScalarTower.toAlgHom",
"isIntegral_algHom_iff",
"Algebra",
"RingHom",
"Algebra.toSMul",
"CommRing.toCommSemiring",
"Iff",
"IsIntegral",
"RingHom.instFunLike",
"Function.Injective",
"CommRing.toRing",
"Semi... | true |
AlgebraicGeometry.SheafedSpace.comp_hom_c_app' | Mathlib.Geometry.RingedSpace.SheafedSpace | [
"Opposite",
"AlgebraicGeometry.SheafedSpace",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"TopCat.instCategoryPresheaf",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"TopCat.Presheaf",
"Pr... | true |
_private.Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace.0.Besicovitch.SatelliteConfig.exists_normalized_aux3._simp_1_4 | Mathlib.MeasureTheory.Covering.BesicovitchVectorSpace | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
inner_gradientWithin_left | Mathlib.Analysis.Calculus.Gradient.Basic | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"Semiring.toModule",
"NormedRing.toRing",
"Inner.inner",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"Pse... | true |
dimH_orthogonalProjection_le | Mathlib.Topology.MetricSpace.HausdorffDimension | [
"LipschitzWith.dimH_image_le",
"InnerProductSpace.toNormedSpace",
"Submodule",
"instEMetricSpaceSubtype",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Mem... | true |
Nat.zero_shiftRight | Init.Data.Nat.Lemmas | [
"Nat.brecOn",
"instOfNatNat",
"instHShiftRightOfShiftRight",
"Nat.instShiftRight",
"Nat.zero_shiftRight._f",
"HShiftRight.hShiftRight",
"Nat",
"OfNat.ofNat",
"Eq"
] | true |
Mathlib.Meta.Positivity.evalAddNorm | Mathlib.Analysis.Normed.Group.Basic | [
"Qq.QuotedDefEq",
"Pure.pure",
"Lean.instantiateMVars",
"Lean.MonadError.mk",
"Qq.findLocalDeclWithTypeQ?",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.mkFreshLevelMVar",
"Qq.trySynthInstanceQ",
"Lean.MetavarKind.natural",
"Mathlib.Meta.Positivity.Strictness",
"Mathlib.Meta.Positivity.Pos... | true |
CategoryTheory.Limits.coconeEquivalenceOpConeOp._proof_1 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CoconeMorphism.w",
"CategoryTheory.Limits.Cocone",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"CategoryTheory... | false |
CategoryTheory.Limits.IsZero.isoZero | Mathlib.CategoryTheory.Limits.Shapes.ZeroObjects | [
"CategoryTheory.Limits.isZero_zero",
"CategoryTheory.Iso",
"CategoryTheory.Limits.IsZero.iso",
"CategoryTheory.Limits.HasZeroObject",
"CategoryTheory.Limits.IsZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"CategoryTheory.Limits.HasZeroObject.zero'",
"CategoryTheory.Category"
] | true |
FreeMonoid.length_eq_four | Mathlib.Algebra.FreeMonoid.Basic | [
"List.length_eq_four",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"Equiv.instEquivLike",
"HMul.hMul",
"Monoid.toMulOneClass",
"FreeMonoid.instCancelMonoid",
"Exists",
"Equiv",
"MulOne.toMul",
"instOfNatNat",
"List",
"MulOneClass.toMulOne",
"Iff",
"FreeMonoid.toList",
"Nat",
"F... | true |
Lean.instBEqReducibilityStatus.beq | Lean.ReducibilityAttrs | [
"instBEqOfDecidableEq",
"BEq.beq",
"Lean.ReducibilityStatus.ctorIdx",
"Nat",
"Bool",
"instDecidableEqNat",
"Lean.ReducibilityStatus"
] | true |
Std.TreeMap.Raw.getElem!_ofList_of_contains_eq_false | Std.Data.TreeMap.Raw.Lemmas | [
"Inhabited.default",
"List.map",
"List.contains",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Std.TreeMap.Raw.ofList",
"Std.TransCmp",
"Prod.fst",
"Std.TreeMap.Raw",
"List",
"Std.DTreeMap.Raw.Const.get!_ofList_of_contains_eq_false",
"Std.LawfulBEqCmp",
"Bool",
"Inhab... | true |
SemidirectProduct.congr'_apply_left | Mathlib.GroupTheory.SemidirectProduct | [
"MulEquiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct.congr'._proof_2",
"SemidirectProduct",
"MulAut.instGroup",
"SemidirectProduct.instMul",
"MulEquiv.instMulEquivClass",
"Group",
"MulAut",
"MulOne.toMul",
"MonoidHomClass.toMonoidHom",
"MonoidHom.comp",
"DivInv... | true |
Booleanisation.instPartialOrder | Mathlib.Order.Booleanisation | [
"Booleanisation",
"Booleanisation.instPreorder",
"PartialOrder",
"Booleanisation.instPartialOrder._proof_1",
"GeneralizedBooleanAlgebra",
"PartialOrder.mk"
] | true |
Module.Relations.Solution.ofπ.congr_simp | Mathlib.Algebra.Module.Presentation.Basic | [
"Semiring.toModule",
"Finsupp.module",
"Ring.toNonAssocRing",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Eq.rec",
"AddCommGroup",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Module.Relations.Solution",
"Module.Relations.relation",
"SubtractionMonoid.toSubNegZeroMonoid",
... | true |
right_le_midpoint | Mathlib.LinearAlgebra.AffineSpace.Ordered | [
"two_inv_lt_one",
"invertibleTwo",
"MulZeroClass.toMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.invOf",
"IsStrictOrderedRing",
"Preorder.toLE",
"... | true |
CochainComplex.ιMapBifunctor.congr_simp | Mathlib.Algebra.Homology.BifunctorShift | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.ιMapBifunctor",
"CategoryTheory.Functor.category",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCa... | true |
OneHomClass.toOneHom.eq_1 | Mathlib.Algebra.Group.Hom.Defs | [
"OneHomClass.map_one",
"One",
"OneHom.mk",
"OneHomClass.toOneHom",
"OneHomClass",
"OneHom",
"Eq.refl",
"Eq",
"DFunLike.coe",
"FunLike"
] | true |
Lean.Meta.pp.showLetValues.threshold | Lean.Meta.PPGoal | [
"Inhabited.default",
"Lean.Option",
"instInhabitedNat",
"Nat",
"Lean.instInhabitedOption"
] | true |
BooleanAlgebra.lt._inherited_default | Mathlib.Order.BooleanAlgebra.Defs | [
"id",
"And",
"Not"
] | false |
Finset.map_comp_coe_apply | Mathlib.Data.Finset.Functor | [
"Multiset.toFinset",
"Finset.functor",
"Finset",
"Multiset.functor",
"Classical.propDecidable",
"Function.comp",
"Multiset",
"Finset.map_comp_coe",
"congrFun",
"Eq",
"Finset.image",
"Functor.map"
] | true |
Algebra.SubmersivePresentation.jacobian_isUnit | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra.SubmersivePresentation.toPreSubmersivePresentation",
"Finite",
"IsUnit",
"Algebra",
"Algebra.PreSubmersivePresentation.jacobian",
"CommRing.toCommSemiring",
"Algebra.SubmersivePresentation",
"Semiring.toMonoid"
] | true |
Pi.mulActionWithZero._proof_1 | Mathlib.Algebra.GroupWithZero.Action.Pi | [
"instHSMul",
"SMulWithZero.toSMulZeroClass",
"Pi.smulWithZero",
"Pi.instZero",
"MulActionWithZero",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"Zero.toOfNat0",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"MulActionWithZero.toSMulWithZero... | false |
ENNReal.holderTriple_coe_iff._simp_1 | Mathlib.Data.Real.ConjExponents | [
"ENNReal.holderTriple_coe_iff",
"ENNReal.ofNNReal",
"NNReal",
"Ne",
"NNReal.instZero",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"ENNReal.HolderTriple",
"NNReal.HolderTriple"
] | false |
_private.Init.Data.BitVec.Lemmas.0.BitVec.append_assoc'._proof_1 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lean.Omega.LinearCombo.coordinate_eva... | false |
MulActionHom.congr_fun | Mathlib.GroupTheory.GroupAction.Hom | [
"DFunLike.congr_fun",
"SMul",
"instFunLikeMulActionHom",
"MulActionHom",
"Eq",
"DFunLike.coe"
] | true |
Partition.mk.inj | Mathlib.Order.Partition.Basic | [
"sSupIndep",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Partition.mk.noConfusion",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"Partition",
"Bound... | true |
ENNReal.eventuallyEq_of_toReal_eventuallyEq | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"ENNReal.toReal_eq_toReal_iff'",
"Eq.mpr",
"Real",
"congrArg",
"Filter.Eventually",
"setOf",
"Membership.mem",
"Filter.mp_mem",
"Filter.EventuallyEq",
"id",
"Ne",
"ENNReal.toReal",
"ENNReal",
"propext",
"ENNReal.instTop",
"Top.top",
"Eq.symm",
"Eq",
"Set.instMembership",
"Filte... | true |
PartialEquiv.symm | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv.right_inv'",
"PartialEquiv.map_source'",
"PartialEquiv.target",
"PartialEquiv",
"PartialEquiv.left_inv'",
"PartialEquiv.source",
"PartialEquiv.invFun",
"PartialEquiv.toFun",
"PartialEquiv.mk",
"PartialEquiv.map_target'"
] | true |
Std.ExtDHashMap.Const.contains_modify | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.Const.modify",
"Std.ExtDHashMap.contains",
"Std.ExtDHashMap.inductionOn",
"LawfulHashable",
"EquivBEq",
"Std.ExtDHashMap",
"Bool",
"Std.DHashMap.Const.contains_modify",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap"
] | true |
deriv_fun_finset_prod | Mathlib.Analysis.Calculus.Deriv.Mul | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"NormedRing.toRing",
"NormedCommRing",
"CommSemiring.toSemiring",
"DifferentiableAt",
"Finset",... | true |
Wbtw.neg | Mathlib.Analysis.Convex.Between | [
"Iff.mpr",
"NegZeroClass.toNeg",
"AddCommGroup.toAddCommMonoid",
"Wbtw",
"AddCommGroup.toAddGroup",
"PartialOrder",
"AddCommGroup",
"addGroupIsAddTorsor",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Module",
"AddCom... | true |
Polynomial.map_modByMonic | Mathlib.Algebra.Polynomial.Div | [
"RingHom",
"Polynomial.divByMonic",
"Polynomial",
"Polynomial.Monic",
"And.right",
"Polynomial.modByMonic",
"Polynomial.map",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"Ring",
"Polynomial.map_mod_divByMonic"
] | true |
_private.Mathlib.Tactic.Linter.FindDeprecations.0.Mathlib.Tactic.getDeprecatedInfo.match_1 | Mathlib.Tactic.Linter.FindDeprecations | [
"_private.Mathlib.Tactic.Linter.FindDeprecations.0.Mathlib.Tactic.getDeprecatedInfo._sparseCasesOn_1",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Name",
"Option"
] | false |
Lean.Elab.Tactic.Do.Context.simpCtx | Lean.Elab.Tactic.Do.VCGen.Basic | [
"Lean.Elab.Tactic.Do.Context",
"Lean.Meta.Simp.Context"
] | true |
RingCon.quotientKerEquivOfSurjective | Mathlib.RingTheory.Congruence.Hom | [
"RingCon.instMulQuotient",
"RingCon.quotientKerEquivOfSurjective._proof_1",
"RingHom",
"RingCon.ker",
"Distrib.toAdd",
"RingCon.Quotient",
"RingCon.instAddQuotient",
"RingCon.quotientKerEquivOfRightInverse",
"NonAssocSemiring",
"RingHom.instFunLike",
"Distrib.toMul",
"NonAssocSemiring.toNonUni... | true |
InvariantBasisNumber.casesOn | Mathlib.LinearAlgebra.InvariantBasisNumber | [
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"InvariantBasisNumber",
"InvariantBasisNumber.mk",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"InvariantBasisNumber.rec",
"... | false |
Pi.single_op₂ | Mathlib.Algebra.Notation.Pi.Basic | [
"Pi.single",
"funext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Pi.apply_single₂",
"DecidableEq",
"Zero"
] | true |
Std.DTreeMap.Internal.Impl.isEmpty_alter! | Std.Data.DTreeMap.Internal.Lemmas | [
"Option.isNone",
"Std.DTreeMap.Internal.Impl.alter!",
"Std.DTreeMap.Internal.Impl.alter_eq_alter!",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.get?",
"Std.TransOrd",
"HSub.hSub",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.size",
"Bool.and",
... | true |
_private.Mathlib.Data.Multiset.Sym.0.Multiset.setOf_mem_sym2._simp_1_1 | Mathlib.Data.Multiset.Sym | [
"Sym2.mk",
"Membership.mem",
"Multiset.mk_mem_sym2_iff",
"Multiset",
"Multiset.instMembership",
"And",
"Multiset.sym2",
"propext",
"Eq",
"Sym2"
] | false |
ENNReal.inv_three_add_inv_three | Mathlib.Data.ENNReal.Inv | [
"Eq.mpr",
"ENNReal.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.instAdd",
"Mathlib.Meta.NormNum.isNat_add",
"ENNReal.ofNat_ne_top",
"Mathlib.Tactic.Ring.Common.mul_congr",
"HMul.hMul",
"Mathlib.Tactic.Ring.Common.add_pf_add_overlap",
"Nat.rawCast",
"ENNReal.instAddComm... | true |
ULift.nonAssocSemiring._proof_2 | Mathlib.Algebra.Ring.ULift | [
"MulOne.toOne",
"HMul.hMul",
"MulOneClass.mul_one",
"ULift",
"MulOne.toMul",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"NonAssocSemiring",
"One.toOfNat1",
"ULift.mulOneClass",
"OfNat.ofNat",
"Eq",
"instHMul"
] | false |
Aesop.Options'.generateScript | Aesop.Options.Internal | [
"Aesop.Options'",
"Bool"
] | true |
CategoryTheory.Preadditive.comp_sub_assoc | Mathlib.CategoryTheory.Preadditive.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Preadditive",
"SubNegMonoid.toSub",
"instHSub",
"AddGroup.toSubNegMonoid",
"Cate... | true |
RingQuot.instSub | Mathlib.Algebra.RingQuot | [
"AddGroupWithOne.toAddGroup",
"Quot.map₂",
"Sub.mk",
"RingQuot.Rel",
"RingQuot",
"SubNegMonoid.toSub",
"AddGroup.toSubNegMonoid",
"RingQuot.mk",
"Sub.sub",
"RingQuot.Rel.sub_right",
"RingQuot.Rel.sub_left",
"Quot",
"Ring.toSemiring",
"Ring",
"Ring.toAddGroupWithOne",
"_private.Mathlib.... | true |
_private.Mathlib.Algebra.Homology.Augment.0.ChainComplex.augment.match_3.eq_3 | Mathlib.Algebra.Homology.Augment | [
"Eq.mpr",
"Unit.unit",
"False",
"Decidable.casesOn",
"ChainComplex.augment._sparseCasesOn_3",
"ChainComplex.augment._sparseCasesOn_3.else_eq",
"Nat.ne_of_beq_eq_false",
"congrArg",
"False.elim",
"Decidable",
"_private.Mathlib.Algebra.Homology.Augment.0.ChainComplex.augment.match_3.splitter._spar... | true |
Lean.Order.instPartialOrderStateRefT' | Init.Internal.Order.Basic | [
"StateRefT'",
"Lean.Order.PartialOrder",
"ST.Ref",
"Lean.Order.instOrderPi"
] | true |
getElem_congr_coll | Init.GetElem | [
"GetElem",
"HEq.refl",
"Eq.rec",
"Eq.casesOn",
"GetElem.getElem",
"eq_of_heq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq"
] | true |
AlgebraicGeometry.RingedSpace.mem_top_basicOpen._simp_1 | Mathlib.Geometry.RingedSpace.Basic | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Lattice.toSemilatticeSup",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"Comm... | false |
QuadraticMap.IsOrtho.symm | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"CommSemiring.toSemiring",
"QuadraticMap.isOrtho_comm",
"AddCommMonoid",
"CommSemiring",
"Iff.mp",
"Module",
"QuadraticMap",
"QuadraticMap.IsOrtho"
] | true |
QuadraticMap.IsometryEquiv.map_negDef_iff | Mathlib.LinearAlgebra.QuadraticForm.Signature | [
"NegZeroClass.toNeg",
"Submodule",
"QuadraticMap.instNeg",
"RingHomSurjective.ids",
"CommRing",
"Preorder.toLT",
"Semiring.toModule",
"SemilinearMapClass.distribMulActionSemiHomClass",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"QuadraticMap.IsometryEquiv.instEquivL... | true |
Lean.Elab.Term.Quotation.HeadCheck._sizeOf_1 | Lean.Elab.Quotation | [
"Option._sizeOf_inst",
"Lean.Syntax._sizeOf_inst",
"Lean.Syntax",
"Lean.Elab.Term.Quotation.HeadCheck.rec",
"Lean.Elab.Term.Quotation.HeadCheck",
"instOfNatNat",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"List._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOf... | false |
Mathlib.Meta.FunProp.LambdaTheorems.mk.noConfusion | Mathlib.Tactic.FunProp.Theorems | [
"instHashableProd",
"Mathlib.Meta.FunProp.LambdaTheoremType",
"id",
"Mathlib.Meta.FunProp.LambdaTheorems.mk",
"Std.HashMap",
"Array",
"instBEqProd",
"Mathlib.Meta.FunProp.LambdaTheorem",
"Lean.Name",
"Mathlib.Meta.FunProp.LambdaTheorems.noConfusion",
"Prod",
"Mathlib.Meta.FunProp.LambdaTheorem... | false |
Ideal.map_includeRight_eq | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"RingHomSurjective.ids",
"Submodule.addSubmonoidClass",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"IsScalarTower.right",
"Ideal.submodule_span_e... | true |
Hyperreal.termε | Mathlib.Analysis.Real.Hyperreal | [
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | true |
Filter.map_mul | Mathlib.Order.Filter.Pointwise | [
"HMul.hMul",
"Filter.map",
"Mul",
"MulHomClass",
"Filter.instMul",
"Filter.map_map₂_distrib",
"map_mul",
"Eq",
"DFunLike.coe",
"Filter",
"FunLike",
"instHMul"
] | true |
Pi.smulZeroClass._proof_1 | Mathlib.Algebra.GroupWithZero.Action.Pi | [
"instHSMul",
"SMulZeroClass",
"smul_zero",
"Pi.instZero",
"funext",
"Pi.instSMul",
"Zero.toOfNat0",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
Int.fdiv_nonneg | Init.Data.Int.DivMod.Lemmas | [
"instHDiv",
"Int.ofNat_fdiv",
"Exists",
"Eq.rec",
"Int.fdiv",
"HDiv.hDiv",
"Int",
"LE.le",
"Nat.cast",
"Int.eq_ofNat_of_zero_le",
"instOfNat",
"Nat",
"Nat.instDiv",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"Int.instLEInt",
"Int.natCast_nonneg",
"_private.Init.Data.Int.DivMod.Lemmas... | true |
Affine.Simplex.incenter_mem_interior | Mathlib.Geometry.Euclidean.Incenter | [
"Eq.mpr",
"Pi.Function.module",
"lt_add_iff_pos_right",
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.points",
"le_refl",
"False",
"Nat.instMulZeroClass",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Affine.Simplex.interior",
"Semiring.toModule",
"AffineMap.instFunLike",
"Finset.u... | true |
_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocFrame | Lean.DocString.Extension | [
"_private.Lean.DocString.Extension.0.Lean.VersoModuleDocs.DocFrame.mk"
] | true |
ContDiffOn.absolutelyContinuousOnInterval | Mathlib.MeasureTheory.Function.AbsolutelyContinuous | [
"InnerProductSpace.toNormedSpace",
"instDecidableNot",
"IsOrderedModule.toPosSMulMono",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.toCompactIccSpace",
"Real",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"instAddMonoidWithOneENat",
"Real.lattice",
"of_decide_eq_true",
"NormedSp... | true |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_359 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
_private.Mathlib.Analysis.Complex.LocallyUniformLimit.0.TendstoLocallyUniformlyOn.deriv._simp_1_2 | Mathlib.Analysis.Complex.LocallyUniformLimit | [
"imp_true_iff",
"True",
"propext",
"Eq"
] | false |
tprod_apply | Mathlib.Topology.Algebra.InfiniteSum.Constructions | [
"Pi.hasProd",
"Pi.topologicalSpace",
"SummationFilter",
"HasProd",
"HasProd.tprod_eq",
"Multipliable",
"Pi.commMonoid",
"Multipliable.hasProd",
"TopologicalSpace",
"T2Space",
"Iff.mp",
"tprod",
"SummationFilter.NeBot",
"Eq.symm",
"Eq",
"CommMonoid"
] | true |
CategoryTheory.Comonad.ForgetCreatesColimits'.liftedCoconeIsColimit._proof_1 | Mathlib.CategoryTheory.Monad.Limits | [
"CategoryTheory.Comonad",
"Eq.mpr",
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.mapCocone_ι_app",
"CategoryTheory.Functor",
"CategoryTheory.Comonad.Coalgebra.a",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.... | false |
HahnSeries.coeff_zero | Mathlib.RingTheory.HahnSeries.Basic | [
"PartialOrder",
"HahnSeries.instZero",
"HahnSeries.coeff",
"Zero.toOfNat0",
"OfNat.ofNat",
"HahnSeries",
"Eq",
"rfl",
"Zero"
] | true |
Combinatorics.Line.casesOn | Mathlib.Combinatorics.HalesJewett | [
"Combinatorics.Line.mk",
"Exists",
"Combinatorics.Line",
"Option.none",
"Combinatorics.Line.rec",
"Eq",
"Option"
] | false |
Descriptive.Tree.mem_pullSub_append._simp_1 | Mathlib.SetTheory.Descriptive.Tree | [
"Membership.mem",
"Subtype",
"Descriptive.tree",
"instHAppendOfAppend",
"List",
"Descriptive.Tree.pullSub",
"CompleteSublattice.instSetLike",
"CompleteSublattice",
"propext",
"CompleteBooleanAlgebra.toCompleteLattice",
"List.instAppend",
"Eq",
"Descriptive.instSetLikeSubtypeSetListMemComplet... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.isEmpty_filter_key_eq_false_iff._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
LinearMap.BilinForm.separatingLeft_toMatrix'_iff._simp_1 | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Pi.Function.module",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"CommRing.toNonUnitalCommRing",
"Matrix.module",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",... | false |
CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan_functor_obj | Mathlib.CategoryTheory.Limits.Constructions.Over.Products | [
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Under.homMk",
"CategoryTheory.Limits.pushoutCoconeEquivBinaryCofan._proof_1",
"CategoryTheory.Under.mk",
"CategoryTheory.Limits.PushoutCocone.inr",
"Catego... | true |
GenLoop.apply_inl_apply_inr_eq_of_mem_boundary_sum | Mathlib.Topology.Homotopy.HomotopyGroup | [
"Real",
"Pi.topologicalSpace",
"congrArg",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"GenLoop.instFunLike",
"Function.comp",
"Membership.mem",
"Cube.boundary",
"Set.Elem",
"Sum",
"Cube.boundary_sum_iff",
"Sum.inl",
"Or.casesOn",
"GenLoop",
"TopologicalSpace",
"Sum.inr",
... | true |
Turing.ToPartrec.Cfg.ret.elim | Mathlib.Computability.TuringMachine.Config | [
"PULift.up",
"Turing.ToPartrec.Cfg.ret",
"Turing.ToPartrec.Cfg.ctorElim",
"Turing.ToPartrec.Cont",
"List",
"Turing.ToPartrec.Cfg.ctorIdx",
"Turing.ToPartrec.Cfg",
"Nat",
"Eq.symm",
"Eq"
] | false |
OrderType.ToType | Mathlib.Order.Types.Defs | [
"LinOrd.carrier",
"Quotient.out",
"LinOrd",
"OrderType.instSetoid",
"OrderType"
] | true |
R0Space.casesOn | Mathlib.Topology.Separation.Basic | [
"R0Space.rec",
"Specializes",
"Symmetric",
"TopologicalSpace",
"R0Space",
"R0Space.mk"
] | false |
SimpleGraph.dist_eq_one_iff_adj._simp_1 | Mathlib.Combinatorics.SimpleGraph.Metric | [
"SimpleGraph.dist",
"SimpleGraph.Adj",
"instOfNatNat",
"SimpleGraph.dist_eq_one_iff_adj",
"SimpleGraph",
"Nat",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Compiler.LCNF.FloatLetIn.dontFloat | Lean.Compiler.LCNF.FloatLetIn | [
"Lean.Compiler.LCNF.FloatLetIn.FloatState.newArms",
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Compiler.LCNF.FloatLetIn.instHashableDecision",
"IO.instMonadLiftSTRealWorldBaseIO",
"modify",
"Lean.Compiler.LCNF.FloatLetIn.FloatM",
"Lean.Compiler.LCNF.FloatLetIn.Decision",
"Lean.Compiler.LCNF.FloatLetIn.Fl... | true |
Std.Http.URI.EncodedString.noConfusionType | Std.Internal.Http.Data.URI.Encoding | [
"Std.Http.URI.IsAllowedEncodedChars",
"Std.Http.URI.EncodedString.casesOn",
"Std.Http.URI.EncodedString",
"Bool",
"ByteArray",
"UInt8",
"Eq"
] | false |
WithTop.instUniqueOfIsEmpty.eq_1 | Mathlib.Order.WithBot | [
"Unique.mk",
"Unique",
"IsEmpty",
"WithTop.inhabited",
"Eq.refl",
"Eq",
"WithTop.instUniqueOfIsEmpty._proof_1",
"WithTop",
"WithTop.instUniqueOfIsEmpty"
] | true |
LinearMap.coe_compAlternatingMap | Mathlib.LinearAlgebra.Alternating.Basic | [
"AlternatingMap",
"LinearMap.instFunLike",
"Function.comp",
"LinearMap",
"AddCommMonoid",
"LinearMap.compAlternatingMap",
"Semiring",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"rfl",
"AlternatingMap.instFunLike"
] | true |
Lean.MonadLog.logMessage | Lean.Log | [
"Lean.MonadLog",
"Lean.Message",
"Unit"
] | true |
Topology.RelCWComplex.isClosed_inter_cellFrontier_succ_of_le_isClosed_inter_closedCell | Mathlib.Topology.CWComplex.Classical.Basic | [
"Iff.mpr",
"Topology.RelCWComplex",
"Eq.mpr",
"Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCell",
"Iff.of_eq",
"congrArg",
"Topology.RelCWComplex.cellFrontier",
"Finset",
"_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.isClosed_inter_cellFrontier_su... | true |
CategoryTheory.Functor.CommShift₂.commShiftFlipObj | Mathlib.CategoryTheory.Shift.CommShiftTwo | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.CommShift₂",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"CategoryTheory.HasShift",
"CategoryTheory.CommShift₂Setup",
"CategoryTheory.Functor.obj",
"CategoryTheory.Functor.CommShif... | true |
Std.Internal.IO.Async.Signal.Waiter._sizeOf_1 | Std.Internal.Async.Signal | [
"Std.Internal.IO.Async.Signal.Waiter",
"instSizeOfDefault",
"instOfNatNat",
"Std.Internal.IO.Async.Signal.Waiter.rec",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"OfNat.ofNat",
"Std.Internal.UV.Signal"
] | false |
_private.Mathlib.Order.KrullDimension.0.Order.krullDim_pos_iff._simp_1_1 | Mathlib.Order.KrullDimension | [
"Preorder.toLT",
"Preorder.toLE",
"isMax_iff_forall_not_lt",
"LT.lt",
"propext",
"Eq.symm",
"Eq",
"Not",
"Preorder",
"IsMax"
] | false |
_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable.0.cond.match_1.eq_2 | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"Unit.unit",
"cond.match_1",
"Bool.true",
"Unit",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
_private.Lean.Compiler.LCNF.ToLCNF.0.Lean.Compiler.LCNF.ToLCNF.toLCNF.etaIfUnderApplied | Lean.Compiler.LCNF.ToLCNF | [
"Inhabited.default",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.ToLCNF.M",
"Lean.Expr",
"Lean.Compiler.LCNF.Purity.pure",
"Nat",
"Inhabited",
"Inhabited.mk"
] | true |
DFinsupp.Lex.addLeftStrictMono | Mathlib.Data.DFinsupp.Lex | [
"CovariantClass.mk",
"add_lt_add_right",
"Preorder.toLT",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"Lex",
"DFinsupp.instLTLex",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"_private.Mathlib.Data.DFinsupp.Lex.0.DFinsupp.Lex.ad... | true |
CategoryTheory.WithInitial.incl.eq_1 | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.incl._proof_1",
"CategoryTheory.WithInitial.incl._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"CategoryTheory.Functor.mk",
"CategoryTheory.WithInitial.incl",
"CategoryTheory.WithInitial",
"... | true |
OrderIso.lowerBounds_image | Mathlib.Order.Bounds.OrderIso | [
"lowerBounds",
"Preorder.toLE",
"OrderIso",
"OrderIso.dual",
"instFunLikeOrderIso",
"OrderIso.upperBounds_image",
"Set.image",
"OrderDual",
"OrderDual.instPreorder",
"Eq",
"DFunLike.coe",
"Preorder",
"Set"
] | true |
Int8.reduceGT._regBuiltin.Int8.reduceGT.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.3529513953._hygCtx._hyg.213 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | [
"IO",
"Sum.inl",
"Bool.true",
"Unit",
"Lean.Meta.Simp.addSEvalprocBuiltinAttr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Int8.reduceGT",
"Lean.Meta.Simp.Simproc"
] | false |
Set.image_op_add | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"AddOpposite",
"AddOpposite.instAdd",
"instHAdd",
"Set.add",
"HAdd.hAdd",
"AddOpposite.op_add",
"Set.image",
"Set.image_image2_antidistrib",
"Eq",
"AddOpposite.op",
"Add",
"Set"
] | true |
Bool.instCommutativeAnd | Init.Data.Bool | [
"Std.Commutative",
"Bool.and",
"Bool",
"Std.Commutative.mk",
"Bool.and_comm"
] | true |
Std.Tactic.BVDecide.BVUnOp.rotateLeft.inj | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVUnOp",
"Std.Tactic.BVDecide.BVUnOp.rotateLeft",
"Nat",
"Std.Tactic.BVDecide.BVUnOp.rotateLeft.noConfusion",
"Eq"
] | true |
instFullPreordCatPreordToCat | Mathlib.Order.Category.Preord | [
"CategoryTheory.Cat.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Full.mk",
"CategoryTheory.Cat.str",
"CategoryTheory.Functor.monotone",
"Preord.instCategory",
"Preord.str",
"CategoryTheory.Cat",
"Preord",
"CategoryTheory.Functor.map",
"CategoryTheo... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.